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arXiv:1408.1550 · International Journal of Quantum Information

Three-slit ghost interference and non-local duality

Mohd Asad Siddiqui

Published Apr 1, 2015• 3 citations
arXivHTMLPDF

Abstract

A three-slit ghost interference experiment with entangled photons is theoretically analyzed using wave-packet dynamics. A non-local duality relation is derived which connects the path distinguishability of one photon to the interference visibility of the other.
DOI
10.1142/s0219749915500227

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The ghost interference observed for entangled photons is theoretically analyzed using wave-packet dynamics. It is shown that ghost interference is a combined effect of virtual double-slit creation due to entanglement, and quantum erasure of which-path information for the interfering photon. For the case where the two photons are of different color, it is shown that fringe width of the interfering photon depends not only on its own wavelength, but also on the wavelength of the other photon which it is entangled with.
The issue of interference and which-way information is addressed in the context of three-slit interference experiments. A new path distinguishability |DQ\mathcal {D}_{Q}DQ​| is introduced, based on unambiguous quantum state discrimination. An inequality connecting the interference visibility and path distinguishability, |V+2DQ3−DQ≤1\mathcal {V} + {2\mathcal {D}_Q\over 3- \mathcal {D}_Q} \le 1V+3−DQ​2DQ​​≤1|⁠, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For two-slit interference, we derive a new duality relation which reduces to Englert's duality relation and the Greenberger–Yasin duality relation, in different limits.
Abstract We perform spectral analysis based on suitable theoretical correlations between V-wave visibility and D-particle distinguishability to verify wave-particle duality in the asymmetrical double-slit experiments. The typical interference spectra obtained in a recent experiment ensure the single-photon approximation in the Fraunhofer far-field condition. The results show that our theoretical model following the complementarity principle is not be consistent with the experimental data at the first main minima of the diffraction distribution where unexpected interference was observed
This thesis is a dissemination of the work I have done in the last four years, under supervision of Prof. Tabish Qureshi. The central theme is towards the understanding of entanglement as a physical resource and looking for its possible applications. This thesis contains six chapters.The Chapter 1 provides the background knowledge for the thesis work, which includes the mathematical formalism of quantum mechanics and the conceptual understanding of entanglement.The Chapter 2 unfolds the idea of fundamental concepts such as Bohr’s complementarity principle, quantum interference, which-path information, their trade-off relation, quantum eraser and also discuss how these issues play their role in building the foundations of quantum theory.The Chapter 3 is devoted to three slit interference experiments. The interference experiment is one of the most prominent concept of quantum theory. The two slit interference set-up is broadly studied and clearly understood, the synopsis for more than two slits are still not clear, recently a focussed research has been shifted towards three slit set-ups. We study the trade-off relation for three slit experiment in terms of visibility and the path distinguishability based on unambiguous quantum state discrimination (UQSD) method.The Chapter 4 discusses the wave-particle duality for multi-slit interference. Several attempts have been made in the past two decades to procure the trade-off relation for multi-slit experiments, yet a satisfactory answer was lacking. We obtain an analogous wave particle duality relation in terms of coherence and path-distinguishability based on UQSD. The role of coherence in building the interference pattern is largely admitted and their amount is readily stated by fringe visibility. Recently coherence has been understood as an information theoretical resource. We explore the measure of coherence as a wave quantifier rather than well known fringe visibility. We also analyze a recently proposed multi-path relation of Bagan et al. which claims to be in Englert’s form. We show that the proposed relation does not hold the essence of complementarity. We also derive a relation similar to Englert’s one to fill the exigency and to explicate its equivalence with our earlier proposed relation.The Chapter 5 discuss the scenario when the source is considered to be entangled. The entangled photon exhibits an interesting phenomenon known as ghost interference. The trade-off relation for two and three slit ghost experiment has been formulated, and also a doable quantum eraser has been proposed.The Chapter 6 aims to use the entanglement as a resource and develop the quantum information technologies, with Quantum Key Distribution (QKD). We propose a QKD protocol using entangled qubits which is shown to add an additional security over the well known BB84 protocol.
Abstract We perform spectral analysis based on suitable theoretical correlations between V-wave visibility and D-particle distinguishability to verify wave-particle duality in asymmetrical double-slit experiments. The typical interference spectra obtained in a recent experiment ensure the single-photon approximation in the Fraunhofer far-field condition. The results show that our theoretical model, following the complementarity principle, is inconsistent with the experimental data at the first main minima of the diffraction distribution, where unexpected interference was observed.